In high school geometry, students are expected to deepen their understanding of geometric shapes and their properties, as well as construct formal mathematical proofs of theorems and geometric relationships. The process of helping students learn to construct a geometric proof can be challenging given the multiple competencies involved (Cirillo…

It is widely recognized that students encounter difficulties with proof across all grades and beyond, yet standardized instruments related specifically to students' perceived self-efficacy for mathematical proof have not been readily available. The purpose of this study was to develop and investigate preliminary validity evidence for a new…

The "proving process" was considered as the stages that should be exist in a proof and in this study, it was aimed to investigate the mathematical proving processes and opinions about proof of gifted students. Case study, one of the qualitative research methods, was used in the study. The research was carried out with the students…

Coming from the commognitive standpoint, we consider proof-based mathematics as a distinct discourse, the transition to which requires special rules for endorsement and rejection of mathematical statements. In this study, we investigate newcomers' learning of these rules when being taught them explicitly. Our data come from academically motivated…

The current study is part of a comprehensive research on linking visualization, students' construction of geometrical concepts and their definitions, and students' ability to prove. The aim of the current study is to investigate the effect of learners' understanding of definitions of geometrical concepts on their understanding of the essence of…

Mathematical justifications offer an approach to which students deepen and extend their mathematical thinking. This process has the potential to enhance students' conceptual understanding. Mathematical practices and process standards ask students to use critical thinking skills to justify their reasoning, but this is usually seen as proofs in high…

With the ever-evolving implementation of technology in the teaching and learning of geometry, the task of designing and/or finding suitable questions or problems that can facilitate and promote mathematical reasoning and accurately assess students' understanding of the subject matter can be a challenge. It is the aim of this article to share the…

It's often useful extending students beyond the limiting geometry of triangles and quadrilaterals to regularly consider generalizations of results for triangles and quadrilaterals to higher order polygons. A brief heuristic description is given here of the author applying this strategy, and which led to an interesting result related to the…

Proof, as a central and integral part of mathematics, is an essential component of mathematical education and is considered as the basic procedure for revealing the truth of mathematical propositions and for teaching productive reasoning as part of human civilization. Is there therefore room for conjectures in mathematics? In this paper after…

We present action research of a problem posed as part of a multi-participant national (Israeli) test checking the mathematical knowledge of high school students at the ages of 16-17, where some of those who solved this problem made an error by using the converse to a well-known theorem, where the converse is not true. In order to examine the…

This study investigated the effects of students' constructions of geometrical concepts related to the circle on their construction and validation of proofs. The participants were 110 high school students. A questionnaire was administered; both qualitative and quantitative methods were used to analyze the results. Afterwards, in-depth interviews…

This study aims to examine the effects of a course module aimed at improving pre-service mathematics teachers' (PMTs) proof schemes. This study used designed-based research. Participants of the course were 22 PMTs in a teacher preparation program. We obtained data from two surveys, one of which consists of proof questions. The other requires…

Learners' difficulties with proof have been ascribed to their lack of understanding of functions that proof performs in mathematics, namely, verification, explanation, communication, discovery, and systematization. However, the extant mathematics education literature on validation of instruments designed to measure learners' beliefs about the…

The topic of recurrence relations has recently been introduced in many discrete mathematics textbooks. Recurrence relations are efficient modelling and problem-solving techniques used in mathematics. Combinatorial problems are often used to introduce recurrence relations. However, many textbooks consider problems that can be reduced only to the…

Proving and refuting are fundamental aspects of mathematical practice that are intertwined in mathematical activity in which conjectures and proofs are often produced and improved through the back-and-forth transition between attempts to prove and disprove. One aspect underexplored in the education literature is the connection between this…